Information on Result #678779
Linear OA(4182, 65597, F4, 28) (dual of [65597, 65415, 29]-code), using construction X applied to Ce(28) ⊂ Ce(20) based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4183, 65598, F4, 28) (dual of [65598, 65415, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4186, 65601, F4, 28) (dual of [65601, 65415, 29]-code) | [i] | ||
| 3 | Linear OA(4187, 65602, F4, 28) (dual of [65602, 65415, 29]-code) | [i] | ||
| 4 | Linear OOA(4182, 54610, F4, 2, 28) (dual of [(54610, 2), 109038, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(4182, 54610, F4, 3, 28) (dual of [(54610, 3), 163648, 29]-NRT-code) | [i] | ||
| 6 | Digital (154, 182, 54610)-net over F4 | [i] | ||
| 7 | Linear OA(4184, 65600, F4, 28) (dual of [65600, 65416, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(4185, 65602, F4, 28) (dual of [65602, 65417, 29]-code) | [i] | ||
| 9 | Linear OA(4186, 65604, F4, 28) (dual of [65604, 65418, 29]-code) | [i] | ||
| 10 | Linear OA(4187, 65606, F4, 28) (dual of [65606, 65419, 29]-code) | [i] | ||
| 11 | Linear OA(4188, 65608, F4, 28) (dual of [65608, 65420, 29]-code) | [i] | ||
| 12 | Linear OOA(4182, 32798, F4, 2, 28) (dual of [(32798, 2), 65414, 29]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(4182, 21865, F4, 3, 28) (dual of [(21865, 3), 65413, 29]-NRT-code) | [i] | ||
| 14 | Linear OOA(4182, 4685, F4, 28, 28) (dual of [(4685, 28), 130998, 29]-NRT-code) | [i] | OA Folding and Stacking | |